Triangle Inequality Flashcard

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

Do the side lengths 2 inches, 2 inches, and 4 inches form a triangle?

Back

No, because 2 + 2 is not greater than 4.

Front

Which of the following lengths cannot represent the sides of a triangle: 32, 34, 60, 28, 30, 58, 13, 20, 27, 2, 4, 5?

Back

28, 30, and 58 cannot represent the sides of a triangle.

Front

List the angles in triangle ABC in order from smallest to largest if the sides are 10 inches, 17 inches, and 16 inches.

Back

∠A, ∠C, ∠B.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the length of side AC?

Back

16 inches.

Front

Can a triangle be formed with side lengths 17, 9, and 30?

Back

No, because 17 + 9 is not greater than 30.

Front

What is the minimum length of a side in a triangle if the other two sides are 5 inches and 7 inches?

Back

The minimum length must be greater than 2 inches (5 - 7).

Front

If two sides of a triangle are 8 inches and 10 inches, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 inches and less than 18 inches (10 - 8 < x < 10 + 8).

Front

What is the relationship between the angles and sides of a triangle?

Back

The largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

Back

It is a right triangle, as it satisfies the Pythagorean theorem (3^2 + 4^2 = 5^2).